Control of Morphology and Substrate Etching in InAs/InP Droplet Epitaxy Quantum Dots for Single and Entangled Photon Emitters

We present a detailed atomic-resolution study of morphology and substrate etching mechanism in InAs/InP droplet epitaxy quantum dots (QDs) grown by metal–organic vapor phase epitaxy via cross-sectional scanning tunneling microscopy (X-STM). Two different etching processes are observed depending on the crystallization temperature: local drilling and long-range etching. In local drilling occurring at temperatures of ≤500 °C, the In droplet locally liquefies the InP underneath and the P atoms can easily diffuse out of the droplet to the edges. During crystallization, the As atoms diffuse into the droplet and crystallize at the solid–liquid interface, forming an InAs etch pit underneath the QD. In long-range etching, occurring at higher temperatures of >500 °C, the InP layer is destabilized and the In atoms from the surroundings migrate toward the droplet. The P atoms can easily escape from the surface into the vacuum, forming trenches around the QD. We show for the first time the formation of trenches and long-range etching in InAs/InP QDs with atomic resolution. Both etching processes can be suppressed by growing a thin layer of InGaAs prior to the droplet deposition. The QD composition is estimated by finite element modeling in combination with X-STM. The change in the morphology of QDs due to etching can strongly influence the fine structure splitting. Therefore, the current atomic-resolution study sheds light on the morphology and etching behavior as a function of crystallization temperature and provides a valuable insight into the formation of InAs/InP droplet epitaxy QDs which have potential applications in quantum information technologies.


Figure.S 1: X-STM current images of the same DEQDs in layer A1 (a and b) and layer A2 (c and d) as shown in
The abrupt change in the current response due to compositional fluctuations and the suppressed topographic contrast makes it easy to identify alloy fluctuations within the QDs meaning that a pure QD (e.g. InAs) should give a uniform contrast in the current image. The point-like features close to the wetting layer are the segregated As atoms. We do not observe any such features inside the QD leading to the conclusion that the QDs are indeed pure without any alloying. The X-STM current images in conjunction with lattice constant measurement and finite element simulations can be used to derive the composition of the material under study.

SII: X-STM Images of QDs on InGaAs layer
As mentioned in the manuscript, growing a thin InGaAs layer suppresses both the etching effects and also the surface As-P exchange preventing the formation of the quasi wetting layer. In the manuscript we presented topographic images of QDs on a 5 nm InGaAs layer crystallized at 520 o C here we show the results from additional experiments by changing the crystallization temperature and also the thickness of the InGaAs layer. A thin layer (1 nm) of InGaAs is sufficient to suppress the etching process at temperatures below and above 500 o C.

SIII: Finite Element Simulation
Simulations were performed with the finite element method (FEM) using the program: COMSOL Multiphysics to model the strain profile and surface relaxation of the quantum dots (QDs). COMSOL is a useful tool to simulate the outward relaxation and the local lattice constant using the solid-mechanics module. This can be applied in the determination of the material composition within a quantum well (QW) or quantum dot (QD) by comparing experimental and simulated results. COMSOL numerically solves differential equations based on continuum elasticity theory. To start the simulation, the program needs a certain geometry of the QD or QW with the appropriate initial strain matrix. The initial strain will deform the cubic volume elements by acting as a force on their surfaces from different directions. The initial strain is caused by the lattice mismatch between the substrate material and the epitaxially grown layers. This lattice mismatch is given by:  The initial strain of a QW is defined to be: where 0 is the lattice mismatch, is the Poisson's ratio (which is a material property), and z is the growth direction 1,2 ; (d) when the material is cleaved, outward pressure is applied to the exposed surface.
This will displace the surface of both the cladding layers and the QW, which is the relaxation that can be experimentally measured with an X-STM.

S5
For a QD, the approach is slightly different, as seen in Figure.S 4. This is due to the change in the shape of the structure. Instead of a full slab, only a small volume with limited dimensions has to be fitted inside the cladding material. Therefore, the lattice constant of the full QD is reduced equally in all three dimensions (x,y,z) by the lattice mismatch to match the lattice constant of the cladding. In matrix form this is written as: The This elasticity matrix is then used in the stress-strain relation as: where the stress and strain are 6×1 vectors: Supporting Information

Figure.S 4:Schematic model of a strained quantum dot at a surface: (a) Two materials with different lattice constants; (b and c) The higher lattice constant of the QD is strained equally in all three dimensions to fit the cladding; (d) Outward relaxation of the cleaved QD.
Some critical steps need to be followed to obtain an accurate result during the FE simulation. First, a large enough box (of cladding material) should be placed around the simulated structure to eliminate non-physical interactions from the boundaries. Second, appropriate boundary conditions should be applied to avoid any error in the simulation. The front side (which will relax outwards) should be set free, the backside is fixed, and the other four surfaces have symmetric or periodic boundary conditions: so, their movement is restricted within their own plane. Third, the initial strain matrix is applied which depends on the shape of the earlier discussed nanostructures (the initial strain matrix varies from QW to QD). In a multi-layered system with various materials, the grown layers are always strained to the substrate material to match the lattice constants. Fourth, a fine enough mesh should be generated to have which can then be compared to the local lattice constant measurements obtained from X-STM experiments.
The main steps for creating a FEM simulation on a cleaved QD are as follows: create a geometry, apply the correct boundary conditions, input the initial strain conditions, and render the mesh. The geometry and mesh can be seen in Figure.S 5. From the X-STM analysis, we know that the QDs have a truncated pyramid shape and the cleaving is parallel to the diagonal of the square base pyramid. As mentioned in the manuscript, DEQDs have a discontinuous wetting layer, for the sake of simplicity, no wetting layer is simulated in FEM, as highlighted in Figure.

SIV: Atom counting method
A filled-state X-STM imaging group V sublattice (P and As atoms) is shown with a line profile along the [100]. The presence of As atoms in the capping layer shows a different height in the STM height profile compared to the background P atoms as shown in Figure.S 6 where 5 individual peaks can be identified due to the presence of As atoms randomly incorporated into the capping layer.

Peaks of As atoms
[100] [110] Figure.S 6:X-STM filled-state image (group V sublattice) is shown with a line profile along [110] direction showing the peaks due to surface and subsurface As atoms randomly incorporated into the capping layer.
number of As atoms present in each corrugation line and to estimate the concentration of As on each corrugation line in the capping layer. The brightness of the feature is directly proportional to the distance from the surface, atoms on the surface being the brightest. The line profile taken along the [110] direction given in Figure.S 6 shows the height of the bright features relative to the surface. Note that if the concentration goes beyond 10-15% as in the wetting layer (WL) region, it is nearly impossible to differentiate one atom from another. Therefore we counted the As atoms in all layers except the WL region. In this way, the maximum number of As atoms for a given size can be measured, and dividing the same with the available number of lattice sites provides the local As concentration.